Finite Group Databasebeta

← #29582360

Subgroups — #29582360

Order 15616.

628 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840054C211yesmaximal, characteristic, complemented
2C2×#16840049C211yesmaximal, characteristic
3#21450742C211yesmaximal, characteristic
4C2×#16839494C211yesmaximal, characteristic, complemented
5C2×#16839491C211yesmaximal, characteristic
6#21443702C211yesmaximal, characteristic, complemented
7C61×#1956C211yesmaximal, characteristic, complemented
8C2×#14519757—21no—
9C2×C4×Dic122C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16840054—22no—
12#16840054—22no—
13#16840049—22no—
14#16840049—22no—
15C2×#14519710—21no—
16C2×#14519708—21no—
17C2×C4⋊#92418C2211yescharacteristic
18C2×C4⋊#92418C2211yescharacteristic
19C2×#14519700—21no—
20C2×#14519697—21no—
21#16839684—22no—
22#16839663—21no—
23#16839661—21no—
24#16839619—21no—
25#16839494—22no—
26#16839491—22no—
27C2×C4⋊Q8×C61C2211yescharacteristic
28C2×#103×C61—22no—
29C2×C4×C8×C61C2211yescharacteristic
30C61×#384C2211yescharacteristic
31C22×Dic122D411yescharacteristic
32C22×D244D411yescharacteristic
33C22×C4×D61—21no—
34C22×#92418—21no—
35C22×#92418—21no—
36#14519757—42no—
37#14519757—42no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42C4×D244—21no—
43C4×D244—21no—
44C4×D244—21no—
45C4×D244—21no—
46C2×C4⋊Dic61—22no—
47C2×C4⋊Dic61D411yescharacteristic
48C2×C4⋊Dic61D411yescharacteristic
49C2×#11758196—21no—
50C2×#11758198—22no—
51C2×#11758198—21no—
52C2×#11758198—22no—
53C2×C4×Dic61—21no—
54#14519710—24no—
55#14519708—24no—
56C4⋊#92418—21no—
57C4⋊#92418—21no—
58C4⋊#92418D412yes—
59C4⋊#92418D412yes—
60#14519700—24no—
61#14519697—24no—
62#14519684—22no—
63C22×Q8×C61—21no—
64C22×C8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61—21no—
67C4⋊Q8×C61—21no—
68C4⋊Q8×C61D412yes—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61D412yes—
74C2×C42×C61C2311yescharacteristic
75#103×C61—44no—
76C4×C8×C61—21no—
77C4×C8×C61—21no—
78C23×D61—21no—
79C2×Q8×C61—22no—
80C2×Q8×C61—42no—
81C2×Q8×C61—42no—
82C2×Q8×C61—41no—
83C22×C4×C61—22no—
84C22×C4×C61—41no—
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C2×D244—21no—
92C2×D244—21no—
93C2×D244—21no—
94C2×D244—21no—
95C2×D244—21no—
96C2×D244Q1612yes—
97C2×C4×D61—41no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C2×C4×D61—41no—
103C2×Dic122—21no—
104C2×Dic122—21no—
105C2×Dic122—21no—
106C2×Dic122—21no—
107C2×Dic122—21no—
108C2×Dic122SD1612yes—
109C2×C8×C61—22no—
110C2×C8×C61—41no—
111C2×C8×C61—41no—
112C4⋊C4×C61—22no—
113C4⋊C4×C61—22no—
114C4⋊C4×C61—42no—
115C4⋊C4×C61—41no—
116C4⋊C4×C61—41no—
117C4⋊C4×C61—41no—
118C4⋊C4×C61—41no—
119C4⋊C4×C61—41no—
120C4⋊C4×C61—41no—
121C42×C61C2×D411yescharacteristic
122C42×C61C2×D411yescharacteristic
123C42×C61C2×D411yescharacteristic
124C42×C61#4111yescharacteristic
125#11758198—44no—
126#11758198—41no—
127#11758198—41no—
128#11758198—82no—
129C4⋊Dic61—21no—
130C4⋊Dic61—21no—
131C4⋊Dic61—21no—
132C4⋊Dic61—21no—
133C4⋊Dic61—44no—
134#11758196—41no—
135#11758196—41no—
136C4×Dic61—41no—
137C4×Dic61—41no—
138C2×#92418—22no—
139C2×#92418—22no—
140C2×#92418—41no—
141C2×#92418—41no—
142C2×#92418—41no—
143C2×#92418—41no—
144C23×C61#12011yescharacteristic
145C22×D61—22no—
146C22×D61—41no—
147C22×D61—41no—
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—41no—
152Q8×C61—44no—
153Q8×C61—82no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—42no—
157C2×C4×C61—42no—
158C2×C4×C61—42no—
159C2×C4×C61—42no—
160C2×C4×C61—81no—
161C2×C4×C61—81no—
162C2×C4×C61#12011yescharacteristic
163C2×C4×C61#12011yescharacteristic
164C2×C4×C61#12111yescharacteristic
165C2×C4×C61#12111yescharacteristic
166C2×C4×C61#12111yescharacteristic
167C2×C4×C61#12711yescharacteristic
168C2×C4×C61C2×SD1611yescharacteristic
169C2×C4×C61C2×Q1611yescharacteristic
170C2×C4×C61#13511yescharacteristic
171C2×C4×C61#13511yescharacteristic
172C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C61#13711yescharacteristic
174C2×C4×C61#13711yescharacteristic
175C2×C4×C61#13711yescharacteristic
176C2×Dic61—22no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185D244—22no—
186D244—22no—
187D244—41no—
188D244—41no—
189C4×D61—81no—
190C4×D61—81no—
191C4×D61—81no—
192C4×D61—81no—
193Dic122—22no—
194Dic122—22no—
195Dic122—41no—
196Dic122—41no—
197C8×C61—42no—
198#92418—42no—
199#92418—42no—
200#10236—611nomaximal, Sylow
201C22×C61#39211yescharacteristic
202C22×C61#45011yescharacteristic
203C22×C61#45111yescharacteristic
204C22×C61#45211yescharacteristic
205C22×C61#45211yescharacteristic
206C22×C61#45311yescharacteristic
207C22×C61#45411yescharacteristic
208C2×D61—42no—
209C2×D61—42no—
210C2×D61—42no—
211C2×D61—81no—
212C2×D61—81no—
213C2×D61—81no—
214C2×D61—81no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—82no—
218C4×C61—82no—
219C4×C61#44811yescharacteristic
220C4×C61#44911yescharacteristic
221C4×C61#45111yescharacteristic
222C4×C61#45211yescharacteristic
223C4×C61#46511yescharacteristic
224C4×C61#46711yescharacteristic
225C4×C61#46811yescharacteristic
226C4×C61#47011yescharacteristic
227Dic61—42no—
228Dic61—81no—
229Dic61—81no—
230C2×#477—611no—
231C2×#476—611no—
232#2538—611no—
233#1956D6111yescharacteristic, complemented
234C2×Q8⋊C8—611no—
235C2×D4⋊C8—611no—
236#1296—611no—
237C2×C61#163111yescharacteristic
238C2×C61#163211yescharacteristic
239C2×C61#163711yescharacteristic
240C2×C61#163811yescharacteristic
241C2×C61#200011yescharacteristic
242C2×C61#200111yescharacteristic
243C2×C61#200611yescharacteristic
244D61—82no—
245C2×C4⋊Q8C2×D6111yescharacteristic
246C2×C22⋊Q8—1221no—
247C2×C4×Q8—611no—
248C2×C4×D4—611no—
249#477—1222no—
250#477—1222no—
251#476—1222no—
252#476—1222no—
253C2×#107—1221no—
254C2×#106—1221no—
255C2×C4⋊C8—611no—
256C2×C4⋊C8—611no—
257C2×#103—22no—
258C2×#103—1221no—
259C2×#102—1221no—
260C2×C4×C8C2×D6111yescharacteristic
261#396—1222no—
262#390—1221no—
263#389—1221no—
264#384C2×D6111yescharacteristic
265#380—1221no—
266Q8⋊C8—1222no—
267D4⋊C8—1222no—
268C61#1023611yescharacteristic, complemented, Sylow
269C22×Q8—21no—
270C22×Q8—611no—
271C22×D4—611no—
272C23×C4—1221no—
273C22×C8—21no—
274C22×C8—1221no—
275C22×C8—1221no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8D24412yes—
280C22⋊Q8—2442no—
281C22⋊Q8—2442no—
282C4×Q8—1221no—
283C4×Q8—1221no—
284C4×Q8—1221no—
285C4×Q8—1221no—
286C4×D4—1221no—
287C4×D4—1221no—
288C4×D4—1221no—
289C4×D4—1221no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—611no—
295C2×C4⋊C4—611no—
296C2×C4⋊C4—1222no—
297C2×C4⋊C4—1221no—
298C2×C4⋊C4C22⋊D6112yes—
299C2×C22⋊C4—1222no—
300C2×C22⋊C4—1222no—
301C2×C22⋊C4—1221no—
302C2×C42—1221no—
303C2×C42C22×D6111yescharacteristic
304#107—1224no—
305#106—1224no—
306C4⋊C8—612no—
307C4⋊C8—612no—
308C4⋊C8—1221no—
309C4⋊C8—1221no—
310#103—44no—
311#103—1224no—
312#102—1224no—
313C4×C8—21no—
314C4×C8—21no—
315#95—1222no—
316C24—1221no—
317C2×Q8—22no—
318C2×Q8—42no—
319C2×Q8—42no—
320C2×Q8—41no—
321C2×Q8—612no—
322C2×Q8—1221no—
323C2×Q8—1221no—
324C2×Q8—1221no—
325C2×Q8—1221no—
326C2×Q8—1221no—
327C2×D4—612no—
328C2×D4—1221no—
329C2×D4—1221no—
330C2×D4—1221no—
331C2×D4—1221no—
332C2×D4—1221no—
333C22×C4—22no—
334C22×C4—41no—
335C22×C4—1221no—
336C22×C4—1221no—
337C22×C4—1221no—
338C22×C4—2441no—
339C22×C4—2441no—
340C22×C4—2441no—
341C22×C4—2441no—
342C22×C4—2441no—
343C22×C4—2441no—
344C22×C4D4×D6111yescharacteristic
345C22×C4D4×D6111yescharacteristic
346C22×C4C2×C22⋊D6111yescharacteristic
347C2×C8—22no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—1222no—
351C2×C8—1222no—
352C2×C8—2441no—
353C2×C8—2441no—
354C2×C8—2441no—
355C2×C8—2441no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—42no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—1221no—
366C4⋊C4—1221no—
367C4⋊C4—1221no—
368C4⋊C4—1221no—
369C4⋊C4—2444no—
370C4⋊C4—2441no—
371C4⋊C4—2441no—
372C22⋊C4—4882no—
373C22⋊C4—2444no—
374C22⋊C4—2441no—
375C22⋊C4—2441no—
376C42—2441no—
377C42—2441no—
378C42C2×D24411yescharacteristic
379C42#1175822211yescharacteristic
380C42D4×D6111yescharacteristic
381C42D4×D6111yescharacteristic
382C23—1222no—
383C23—2441no—
384C23—2441no—
385C23—2441no—
386C23—2441no—
387C23—2441no—
388C23—2441no—
389C23#1451974511yescharacteristic
390Q8—44no—
391Q8—82no—
392Q8—1222no—
393Q8—1222no—
394Q8—2441no—
395Q8—2441no—
396D4—1222no—
397D4—1222no—
398D4—2441no—
399D4—2441no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—1222no—
409C2×C4—4881no—
410C2×C4—4881no—
411C2×C4—4881no—
412C2×C4—4881no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4#1451974711yescharacteristic
422C2×C4#1451974711yescharacteristic
423C2×C4#1451975011yescharacteristic
424C2×C4#1451975011yescharacteristic
425C2×C4#1451975111yescharacteristic
426C2×C4#1451977311yescharacteristic
427C2×C4SD16×D6111yescharacteristic
428C2×C4Q16×D6111yescharacteristic
429C2×C4#1451979811yescharacteristic
430C2×C4#1451980011yescharacteristic
431C2×C4#1451980411yescharacteristic
432C2×C4#1451980611yescharacteristic
433C2×C4#1451980911yescharacteristic
434C2×C4#1451980911yescharacteristic
435C8—42no—
436C8—2442no—
437C8—2442no—
438C22—4881no—
439C22—4881no—
440C22—4881no—
441C22—4881no—
442C22—2442no—
443C22—2442no—
444C22—2442no—
445C22#1683967111yescharacteristic
446C22#1683991111yescharacteristic
447C22#1683991611yescharacteristic
448C22#1683992111yescharacteristic
449C22#1683992311yescharacteristic
450C22#1683992911yescharacteristic
451C22#1683993411yescharacteristic
452C4—21no—
453C4—21no—
454C4—82no—
455C4—82no—
456C4—4881no—
457C4—4881no—
458C4—2442no—
459C4#1683990211yescharacteristic
460C4#1683991011yescharacteristic
461C4#1683991911yescharacteristic
462C4#1683992711yescharacteristic
463C4#1683999411yescharacteristic
464C4#1684000211yescharacteristic
465C4#1684001111yescharacteristic
466C4#1684001911yescharacteristic
467C2—4882no—
468C2#2144494311yescharacteristic
469C2#2144495011yescharacteristic
470C2#2144498111yescharacteristic
471C2#2144498811yescharacteristic
472C2#2144682111yescharacteristic
473C2#2144682811yescharacteristic
474C2#2144686011yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1956C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1956D61
hypocenterC61#10236
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16840054C2semidirect
4. C2×#16839494C2semidirect
6. #21443702C2semidirect
7. C61×#1956C2semidirect
233. #1956D61semidirect
268. C61#10236semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168400542
C2×#168400492
#214507422
C2×#168394942
C2×#168394912
#214437022
C61×#19562
#1023661